1. Field of the Invention
This invention relates to the field of data communications systems. More specifically, it relates to the field of wired communications systems. Even more specifically, it relates to a method and apparatus for providing compensation or equalization for the frequency response of a transmission line.
2. The Prior Art
At some point in any data communications system, the signal to be communicated passes through an electrical conductor. This electrical conductor can take many forms such as, for example, a coaxial cable ("coax"), an unshielded twisted pair cable ("UTP"), or a shielded twisted pair cable ("STP"). Such conductors are known generally as transmission media or transmission lines. Most transmission lines such as these exhibit a low pass characteristic. That is, they transmit low frequency components of the signal more readily than high frequency components of the signal, i.e., their frequency response is not "flat".
Most communications signals consist of symbols that represent the information to be communicated. These symbols are usually packed close to one another in the time domain in order to achieve the highest transmission speeds. However, when a signal such as this is passed through a transmission line having other than a flat frequency response, the low pass characteristic of the transmission line has the effect of widening each symbol in time. This widening can result in spill over or inter-symbol interference among symbols of the signal. This in turn can result in the loss of, or incorrect communication of information.
To compensate for the low pass characteristic of a transmission line, the signal is typically passed through a transmission line equalizer at the receiver end of the transmission line. The transmission line equalizer exhibits a high pass characteristic. That is, it transmits high frequency components of the signal more readily than the low frequency components of the signal and therefore exhibits an inverse frequency response to that of the transmission line. When put in series with the low pass frequency response of the transmission line, the high pass frequency response of the transmission line equalizer has the effect of returning each symbol to its original form. The information to be communicated is thereby preserved.
The exact low pass characteristic of the transmission line depends in part on the specific media used and in part on the length of the transmission line. So, if these factors vary within a particular application of a communications system, the transmission line equalizer will have to be able to adapt to these differences in order to correctly compensate for the effect of the transmission line on the signal.
It is important that the transmission line equalizer provides just the right amount of compensation to avoid under-compensation (the failure to remove some residual inter-symbol interference that continues to cause the loss of or incorrect communication of information) or over-compensation (noise enhancement and distortion of the symbols that causes the loss of or incorrect communication of information).
As those of ordinary skill in the art will recognize, the frequency response of any system can be expressed by a polynomial equation referred to as the transfer function of the system. This equation often takes the shape of a fraction with the numerator having one polynomial expression and the denominator having another. The roots of the numerator are referred to as zeros and the roots of the denominator are referred to as poles. These roots correspond to the corner frequencies of the system and can be manipulated by a designer to create a transfer function having a desired frequency response.
In the case of a communications system, the transmission line exhibits one transfer function and the transmission line equalizer attempts to exhibit the exact inverse of that transfer function in order to compensate for the effect of the transmission line on the communicated signal.
In order to achieve successful compensation, two general steps must be accomplished. First, the frequency response of the transmission line must be either determined empirically (i.e., by measurement) or approximated theoretically. Since empirical determination is often cost prohibitive, theoretical approximation is generally the method used. The accuracy of such an approximation will depend in part on the specific media used and the length of the transmission line. Second, the inverse of the frequency response of the transmission line must be exhibited by the transmission line equalizer as configured by the designer. This is accomplished by manipulating the number and location of the roots, poles and zeros of the transfer function of the transmission line equalizer until the desired frequency response is achieved. As noted above, the accuracy of the approximation of the frequency response of the transmission line depends on the specific media used and the length of the transmission line. Hence, the transmission line equalizer should be designed to adapt to changes in either of these factors to assure successful compensation for the signal.
The frequency response of a UTP or STP transmission line due to or dominated by skin effect is usually approximated as having a roll off of 10 dB per decade (10 db/dec).
As discussed before, using this approximation a transmission line equalizer would have to exhibit the inverse frequency response of the transmission line to compensate correctly for the presumed frequency response of the transmission line. Unfortunately, each zero in a transfer function provides a gain of 20 dB/dec above the corner frequency of that zero. This is obviously too much by itself. What is needed is a transfer function with about "half" of the gain of one zero, i.e. 10 dB instead of 20 dB. The prior art has adopted two approaches to reduce this response to more closely approximate the inverse frequency response of the typical transmission line.
The first prior art approach is to design the transmission line equalizer with a pole/zero pair and place the pole at a higher frequency than the zero. The addition of the pole has the effect of partially canceling the gain of the zero. The intended result is for the modified transfer function to have a slope of 10 dB/dec in the frequency range of interest (i.e., the frequency range of the signals to be transmitted over the transmission line).
For an adaptive design, the frequency separation between the pole and zero can be varied to adjust the frequency response of the transmission line equalizer to better match that of the transmission line whatever the specific media used or the length of the transmission line.
FIG. 1A is a representation of a transfer function H(s) where s represents the complex frequency, z is the zero frequency (rad/sec) of the transfer function, and p is the pole frequency (rad/sec) of the transfer function where z is less than p.
FIG. 1B is a plot showing the frequency response of the transfer function H(s) of FIG. 1A. The vertical axis is gain in db (20 loglH(j.omega.)l), the horizontal axis is angular frequency, .omega., in radians per second. The dashed curve is an asymptote of the transfer function H(s). The solid curve is a plot of the transfer function H(s).
The second prior art approach is to add an "all pass" function to a high pass function. An "all pass" function transmits all frequency components of the signal. The addition of the all pass function to the high pass function has the effect of producing a weighted average of the two functions with less high frequency gain than that of the high pass function alone.
The high pass function can have any number of zeros. Recall that one zero produces a gain of 20 dB/dec. This is true of each zero in the function. So at frequencies above the highest corner frequency, a high pass function that has n zeros would exhibit a gain of n x 20 dB/dec.
For an adaptive design, the mixture in the addition function can be varied to adjust the frequency response of the transmission line equalizer to better match that of the transmission media whatever the specific media used or the length of that media. One technique used to vary the mixture is to multiply the output of the high pass function by a selectable constant.
FIG. 2A is a representation of a transfer function E(s) where s represents the complex frequency. H.sub.1 (s) is a high pass transfer function (shown as a second order function specifically here), .omega..sub.n is the natural frequency of H.sub.1 (s), .xi. is the damping factor of H.sub.1 (s), k is the variable gain (between 0 and 1) fitted to the transmission line type and length.
FIG. 2B is a plot of gain versus frequency for four curves A, B, C and D. Curve A is a constant unity gain function. Curve B is the frequency response of H.sub.1 (s). Curves C and D are two different equalizer response curves corresponding to gain value k.sub.1 and k.sub.2, respectively, where k.sub.1 &gt;k.sub.2.
As can be seen, adjusting k.sub.1 in transfer function E(s) between 0 and 1 allows the slopes of curves C and D to be adjusted as desired.
The transmission line equalizers that result from either of the two prior art approaches above can only provide a moderate approximation of the transfer function needed to compensate for the frequency response of the transmission lines in certain specific applications. This is due to inaccuracies in the model used to approximate the frequency response of the transmission media.
One specific application where the prior art transmission line equalizers provide only a rough approximation of the transfer function needed to compensate for the frequency response of the transmission media is for Fast Ethernet Local Area Network (LAN) applications referred to as 100BaseT4 designed to IEEE Standard 802.3u-1995 Clause 23. This is due in part to the wide frequency spread and in part to the advanced coding scheme of the 100BaseT4 standard. The resulting mismatch between the transmission line and the transmission line equalizer degrades the receiver performance to such an extent that it limits the achievable transmission speed and distance.